Emergence of Self-Sustained Oscillations for SIRS Model on Random Networks

Abstract

We study the phase transition from the persistence phase to the extinction phase for
the SIRS (susceptible/ infected/ refractory/ susceptible) model of diseases spreading on
random networks. By studying a temporal evolution and synchronization parameter of
this model on random networks, we nd that, this model on random networks, shows a
synchronization phase in a narrow range of very small values of clustering coecient. This
nding corroborates the conclusion reached in [Phys. Rev. Lett. 86, 2909 (2001)] that,
the clustering coecient is responsible for the emergence of the synchronization phase
in the small world networks. With these results and the result that we had obtained
in [Physica A 535, 122251 (2019)], we give a reasonable justication the reason for the
occurrence of that behavior, at small values of the clustering coeffcient.